Given 2 circles with known radii and positions.
What is the position of the pink circle if it should touch the previous 2 circles and the x-axis?
A little bit more info:
- It is a special case for this one previous related problem. But I find it difficult to represent AD, DB or DC cathetus.
- This also could be useful info probably related problem
Let $C=(x,y)$ be the center of the pink circle, of radius $r_C=y$. Then we have: $$ \cases{ x^2+y^2=(r_B+y)^2\\ x^2+(r_A+r_B-y)^2=(r_A+y)^2} $$ This system is easy to solve for $x$ and $y$.